I would probably warn someone if it seemed likely that other people would make the connection, and that they were making any efforts to hide it. If someone is using something that looks like a real name (something like "Mary Jane Olsen" rather than "MJ_in_Minnesota" or "I love cookies") I'll assume that either they're okay with people associating their real names with their posts, or they decided that "Mary Jane Olsen" would be less conspicuous than "Queen of the May." I've noticed over the years that people who post with odd-seeming names are often assumed to be using handles/pseudonyms, but things that look like ordinary names are taken at face value.
I also wouldn't assume that Person1 was being careful about Person2's identity; if you start blogging as This_is_an_alias but tell a hundred of your closest friends that that's your alias, one of them may offhandedly say here's a cool thing my friend Jay said" and link to the until-them pseudonymous blog. This happened to a friend of mine, ages ago; the person who posted the link hadn't thought that maybe there was a reason that her LiveJournal, unlike his, didn't have her real name on it anywhere. Oh, as a meta-level thing, it's possible that this post contains enough information for someone to guess who I might be, the way "I went to high school with $person" compared with my current location might be. However, that would take a bit of work, unless you're one of a few of my friends, in which case PM me if you want to identify yourself.